Map Color Puzzles
Color every region of a freshly drawn map so that no two regions sharing a border end up the same color.
Hints available. Play as many boards as you like.
Ready when you are.
Scan to open on a phone
Scan for the same board — no hints.
How to play
Tap or click a region to cycle it through the colors on offer and back to blank. On a keyboard, move with the arrow keys and press 1, 2, 3 or 4 to paint the region under the cursor; Backspace clears it.
The only rule is that two regions sharing a border must not share a color. Regions that meet at a single corner do not share a border, so they may match.
A few regions start already colored and cannot be changed — they are drawn with a ring. Every color in the palette appears among them, so you can see each one before you commit to anything.
Each color is a numbered index, not just a hue: it is drawn as a number, a hatch pattern and a fill. The board is fully playable in grayscale.
Strategy
Start at the most crowded region, not the top-left one. A region with six neighbors has the fewest colors available to it, and fixing it first means the rest of the map is being fitted around a decision that was forced rather than guessed.
Look for three regions that all border each other. That triangle needs three different colors, and it usually pins down a whole neighborhood once one of the three is settled.
On a three-color board, work outward in a chain. Any region with two differently colored neighbors has exactly one color left, and following that chain is faster than scanning the whole map after every move.
There is no single right answer, so a color you dislike is not a mistake. If a region strands one of its neighbors, repaint the neighbor rather than starting again — only the border between the two of them was ever wrong.
Difficulty and variants
Easy and medium boards give you four colors, which the four color theorem guarantees is always enough for a flat map. Hard boards hand you three, on a map that genuinely needs all three — which removes almost every free choice and is why the region count matters less than the palette.
Region count climbs with difficulty too: nine regions on easy, thirteen on medium, sixteen on hard, and larger on a tablet-sized board. Every board is generated so that the palette it offers is exactly the number of colors the map requires.
Questions, answered
Is there only one correct way to color the map?
No, and that is the point. Any coloring where no two bordering regions match is accepted, and most boards have many. The puzzle checks the rule, never a stored answer.
Why are four colors always enough?
The four color theorem, proved in 1976: any map drawn on a flat surface can be colored with four colors so that no two regions sharing a border match. Our four-color boards can always be finished; the three-color boards are built so that three really is enough.
Can I play if I have trouble telling colors apart?
Yes. Every color is a numbered index drawn into its region, over a distinct hatch pattern, and the palette key below the board shows all three or four. Nothing on the board depends on hue alone.
Do regions that touch at a corner count as neighbors?
No. Only a shared edge counts, exactly as on a real map, so two regions meeting at a single point may share a color.